GED cheat sheet

Slope of a line through (x1, y1) and (x2, y2): m = (y2 − y1)/(x2 − x1); horizontal lines have slope 0, vertical lines have undefined slope.

Slope-intercept form y = mx + b: m is the rate of change per unit, b is the starting value when x = 0.

Percent change = (new − old)/old × 100; a 20% decrease followed by a 20% increase returns to 96% of the original, not 100%.

Simple interest I = Prt; compound growth A = P(1 + r/n)^(nt), where n is compounding periods per year.

Pythagorean theorem a² + b² = c² applies only to right triangles; the hypotenuse c is always the side opposite the right angle.

Area formulas: rectangle lw, triangle ½bh, circle πr²; volume of a rectangular prism lwh, of a cylinder πr²h.

Mean = sum ÷ count; median is the middle value of an ordered list (average the two middle values when the count is even); range = max − min.

Probability of an event = favorable outcomes ÷ total equally likely outcomes; independent events multiply, as in P(A and B) = P(A) × P(B).

Solve a system by substitution or elimination; a linear system has no solution when the lines are parallel (same slope, different intercepts).

Main idea = the claim the whole passage supports; supporting details answer who, what, when, where, why, or how and can be removed without collapsing the argument.

An argument's conclusion is the statement the author wants accepted; premises are the reasons offered; an unstated assumption is a premise the argument needs but never states.

Evaluate evidence by relevance (does it bear on the claim?), sufficiency (is there enough of it?), and credibility (is the source informed and unbiased?).

Transition words signal structure: however, although, and nevertheless mark contrast; therefore, thus, and consequently mark conclusion; for example marks illustration.

In grammar, a sentence fragment lacks a subject or a complete verb; a run-on joins two independent clauses with no conjunction or punctuation.

Subject-verb agreement: the verb matches the true subject, not a phrase between them - 'The box of tools is heavy,' not 'are heavy.'

Pronoun reference must be unambiguous: a pronoun agrees with its antecedent in number and person, and 'they' cannot refer to a singular noun in formal edited English.

Commas set off nonessential clauses and separate items in a list; a semicolon joins two independent clauses, and a colon introduces a list or explanation.

The extended response is scored on how well it uses evidence from the passage to support a clear, organized argument, not on personal opinion alone.

The U.S. Constitution separates power among legislative (Congress), executive (President), and judicial (courts) branches, with checks and balances among them.

The Bill of Rights comprises the first ten amendments; the First Amendment protects speech, press, assembly, petition, and religion.

Federalism divides authority between the national government and the states; the Supremacy Clause makes federal law supreme over conflicting state law.

The Three-Fifths Compromise counted enslaved people as three-fifths of a person for representation; the Civil War amendments (13th, 14th, 15th) abolished slavery, granted citizenship and equal protection, and protected voting rights.

Supply and demand: a price above equilibrium creates a surplus, a price below equilibrium creates a shortage, and equilibrium occurs where quantity supplied equals quantity demanded.

Gross domestic product measures the total market value of final goods and services produced in a country in a given period.

Push factors drive migration away from a place (war, famine, persecution); pull factors attract migrants (jobs, safety, freedom).

Reading a map: latitude lines run east–west and measure distance north or south of the equator; longitude lines run north–south and measure distance east or west of the prime meridian.

Primary sources are created by participants or witnesses at the time (letters, laws, photographs); secondary sources interpret or analyze those sources afterward.

Cell theory: all living things are made of cells, the cell is the basic unit of life, and cells arise from existing cells.

Photosynthesis converts carbon dioxide and water into glucose and oxygen using light energy; cellular respiration reverses this to release energy (ATP).

Newton's second law F = ma; an object at rest or in uniform motion stays that way unless acted on by a net force (first law).

Density = mass ÷ volume; an object denser than its fluid sinks, and less dense objects float.

In a chemical equation, matter is conserved, so coefficients must balance atoms of each element on both sides.

DNA bases pair A with T and C with G; a mutation is a change in the DNA sequence that may alter protein structure or function.

Natural selection requires variation, heritability, and differential reproductive success across generations.

The water cycle moves water through evaporation, condensation, precipitation, and runoff; energy from the Sun drives the cycle.

In an experiment, the independent variable is manipulated, the dependent variable is measured, and controlled variables are held constant to isolate cause and effect.